EVT and tail-risk modelling: Evidence from market indices and volatility series

Value-at-Risk (VaR) has become the universally accepted risk metric adopted internationally under the Basel Accords for banking industry internal control, capital adequacy and regulatory reporting. The recent extreme financial market events such as the Global Financial Crisis (GFC) commencing in 2007 and the following developments in European markets mean that there is a great deal of attention paid to risk measurement and risk hedging. In particular, to risk indices and attached derivatives as hedges for equity market risk. The techniques used to model tail risk such as VaR have attracted criticism for their inability to model extreme market conditions. In this paper we discuss tail specific distribution based Extreme Value Theory (EVT) and evaluate different methods that may be used to calculate VaR ranging from well known econometrics models of GARCH and its variants to EVT based models which focus specifically on the tails of the distribution. We apply Univariate Extreme Value Theory to model extreme market risk for the FTSE100 UK Index and S&P-500 US markets indices plus their volatility indices. We show with empirical evidence that EVT can be successfully applied to financial market return series for predicting static VaR, CVaR or Expected Shortfall (ES) and also daily VaR and ES using a GARCH(1,1) and EVT based dynamic approach to these various indices. The behaviour of these indices in their tails have implications for hedging strategies in extreme market conditions.     

基于分形理论的原油期货高频交易风险测度研究

为了捕捉原油期货高频波动规律,采用WTI原油期货五分钟数据,基于分形理论分别构建GED分布和Skew-t分布的FIGARCH、FIAPARCH和HYGARCH模型,分析其波动特征并对风险进行测度。结果显示：三种模型均较好地刻画出WTI原油期货波动的长记忆特征;基于Skew-t分布的HYGARCH模型在度量原油期货高频交易风险时尤为精确;多头与空头头寸的VaR呈现非对称性;套期保值者或高频交易者可依据模型预测波动率,防止短期波动率过大导致保证金不足而被强制平仓。高频交易在提高市场流动性和拓宽市场深度方面具有一定的作用,因此,在风险可控的条件下,政府应该鼓励高频交易,促进我国衍生品市场繁荣发展,并增强衍生品市场稳定性和国际竞争力。     

Heterogeneous Traders,the Leverage Effect and Volatility of the Chinese P2P Market

The new financial industry represented by peer-to-peer lending has gradually become a new source of volatility due to the increasing complexity of the Chinese financial market. This volatility leads to greater risk to P2P investors and has become the focus of the regulatory authorities in China. Based on the background data of the P2P platform, Honglingchuangtou, we use the factor analysis method to construct a platform volatility (PV) index and we construct an HAR model to study the heterogeneous traders and leverage effect in the Chinese P2P market. The empirical results show that there are both short-term and long-term heterogeneous traders in the Chinese P2P market and that long-term traders have the greatest impact on market volatility. Similar to traditional financial markets, the volatility of the P2P market also shows a leverage effect, which means that the negative volatility of trader actions should have a negative impact on market fluctuations. With regard to the leverage effect, the LHAR-PV model is superior because of a higher goodness of fit and a lower prediction error.     

Transaction taxes, greed and risk aversion in an agent-based financial market model

Recent agent-based financial market models came to the result that taxing financial transactions does not per se increase financial stability and that the response of volatility and misalignments to rising tax rates seem to be u-shaped. Moreover, greed and the risk appetite of traders are often blamed for financial instability and there is no evidence how greed and risk aversion affect the effectiveness of regulations in financial markets. We aim to add to this gap in the literature by analyzing how the effectiveness of transaction taxes depend on different behavioral patterns within an agent-based framework. Our simulations indicate that a tax rate of 0.1% demarcates the stabilizing tax regime from the destabilizing one. We figure out that transaction taxes are less effective, either when chartists trade more aggressively, fundamentalists trade less aggressively, agents switch more frequently between trading strategies or only have short memory in their fitness measures. Lower risk aversion of agents, however, makes higher tax rates more effective as indicated by a flatter volatility response curve. We conclude that additional regulations should concentrate on the traders’ responsibilities for their risk-exposure.     

基于极值分布理论的VaR与ES度量

本文应用极值分布理论对金融收益序列的尾部进行估计,计算收益序列的在险价值VaR和预期不足ES来度量市场风险。通过伪最大似然估计方法估计的GARCH模型对收益数据进行拟合,应用极值理论中的GPD对新息分布的尾部建模,得到了基于尾部估计产生收益序列的VaR和ES值。采用上证指数日对数收益数据为样本,得到了度量条件极值和无条件极值下VaR和ES的结果。实证研究表明:在置信水平很高(如99%)的条件下,采用极值方法度量风险值效果更好。而置信水平在95%下,其他方法和极值方法结合效果会很好。用ES度量风险能够使我们了解不利情况发生时风险的可能情况。     

Parametric Value-at-Risk analysis: Evidence from stock indices

We evaluate the performance of several volatility models in estimating one-day-ahead Value-at-Risk (VaR) of seven stock market indices using a number of distributional assumptions. Because all returns series exhibit volatility clustering and long range memory, we examine GARCH-type models including fractionary integrated models under normal, Student-t and skewed Student-t distributions. Consistent with the idea that the accuracy of VaR estimates is sensitive to the adequacy of the volatility model used, we find that AR (1)-FIAPARCH (1,d,1) model, under a skewed Student-t distribution, outperforms all the models that we have considered including widely used ones such as GARCH (1,1) or HYGARCH (1,d,1). The superior performance of the skewed Student-t FIAPARCH model holds for all stock market indices, and for both long and short trading positions. Our findings can be explained by the fact that the skewed Student-t FIAPARCH model can jointly accounts for the salient features of financial time series: fat tails, asymmetry, volatility clustering and long memory. In the same vein, because it fails to account for most of these stylized facts, the RiskMetrics model provides the least accurate VaR estimation. Our results corroborate the calls for the use of more realistic assumptions in financial modeling.     

Risk management of precious metals

This paper examines volatility and correlation dynamics in price returns of gold, silver, platinum and palladium, and explores the corresponding risk management implications for market risk and hedging. Value-at-Risk (VaR) is used to analyze the downside market risk associated with investments in precious metals, and to design optimal risk management strategies. We compute the VaR for major precious metals using the calibrated RiskMetrics, different GARCH models, and the semi-parametric Filtered Historical Simulation approach. The best approach for estimating VaR based on conditional and unconditional statistical tests is documented. The economic importance of the results is highlighted by assessing the daily capital charges from the estimated VaRs.     

Spillover effects in oil-related CDS markets during and after the sub-prime crisis

This paper investigates the return and volatility spillover effects across oil-related credit default swaps (CDSs), the oil market, and financial market risks for the US during and after the subprime crises. The empirical analysis is based on monthly return and realized volatility data from February 2004 to April 2020. We estimate both static and dynamic generalized dynamic spillover measures based on vector autoregressive (VAR) models. Our full sample empirical findings show that the oil market is the primary source of risk transmission for all the oil-related credit default swaps, while the bond market is the highest source of risk transmission to the stock market and vice versa. We also provide evidence that the regulated monopoly US utility sector has the least role in volatility transmission. Furthermore, the bailout program conducted by the US Treasury and Federal Reserve helped stabilize the US financial market through the purchase of toxic assets after the subprime financial crisis. We find strong evidence that the federal funds rate hike cycles lessen total risk transmission throughout the US bond market. Finally, our findings assert that oil price shocks have a significant effect on the oil-related CDSs in some sub-periods via the demand and supply transmission channels.     

Asset allocation and multivariate position based trading

I add a second risky asset and a risk free bond to the univariate artificial market investigated by Lux and Marchesi (Int J Theor Appl Finance 3(4):675–702, 2000), keeping track of traders aggregate positions and wealth. Asset allocation and security selection are modeled as separate decision processes, as is common practice in financial institutions. Introducing position based trading avoids inconsistencies in traders inventories resulting from the order based setup of the original model, while preserving its ability to reproduce the stylized facts of financial return series.      

Financially constrained arbitrage in illiquid markets

This article analyzes trading strategies when arbitrageurs impact prices. Trades of financially constrained arbitrageurs are feedback functions of their capital, which depends on the amount traded. A component of arbitrage trading ensures financial flexibility. This hedging component explains why price deviations persist in spite of arbitrage. Financial constraints are responsible for volatile prices and for time variation in the correlations of prices across markets. Distortions arise when regulated firms can influence the dynamics of prices on which capital requirements are based. Under current value at risk (VaR) measures, large traders behave aggressively and have a cost advantage relative to other traders.     

Forecasting value at risk with intra-day return curves

Methods for incorporating high resolution intra-day asset price data into risk forecasts are being developed at an increasing pace. Existing methods such as those based on realized volatility depend primarily on reducing the observed intra-day price fluctuations to simple scalar summaries. In this study, we propose several methods that incorporate full intra-day price information as functional data objects in order to forecast value at risk (VaR). Our methods are based on the recently proposed functional generalized autoregressive conditionally heteroscedastic (GARCH) models and a new functional linear quantile regression model. In addition to providing daily VaR forecasts, these methods can be used to forecast intra-day VaR curves, which we considered and studied with companion backtests to evaluate the quality of these intra-day risk measures. Using high-frequency trading data from equity and foreign exchange markets, we forecast the one-day-ahead daily and intra-day VaR with the proposed methods and various benchmark models. The empirical results suggested that the functional GARCH models estimated based on the overnight cumulative intra-day return curves exhibited competitive performance with benchmark models for daily risk management, and they produced valid intra-day VaR curves.     

An approximate long-memory range-based approach for value at risk estimation

This paper proposes new approximate long-memory VaR models that incorporate intra-day price ranges. These models use lagged intra-day range with the feature of considering different range components calculated over different time horizons. We also investigate the impact of the market overnight return on the VaR forecasts, which has not yet been considered with the range in VaR estimation. Model estimation is performed using linear quantile regression. An empirical analysis is conducted on 18 market indices. In spite of the simplicity of the proposed methods, the empirical results show that they successfully capture the main features of the financial returns and are competitive with established benchmark methods. The empirical results also show that several of the proposed range-based VaR models, utilizing both the intra-day range and the overnight returns, are able to outperform GARCH-based methods and CAViaR models.     

基于GARCH类模型的权证时变VaR值估计

由于权证收益率分布具有尖峰厚尾和非对称性的特征，其市场风险的估算运用GARCH类模型比较合适。本文选取包钢JTB1的日收盘价格序列为样本，分别用EGARCH、TGARCH模型估计样本期间内日VaR值，并进行了比较。结果表明，EGARCH模型较好地预测了损失结果，而TGARCH模型则低估了风险。因此，基于EGARCH模型对VaR值的计算能更好地反映权证收益率的波动特征和准确预计损失，可以为权证的风险管理提供较为可靠的风险度量工具。     

Do real estate investors trade on momentum?

Real estate markets are known to be less-than-efficient for many reasons, but what roles short-term trading plays are unclear. Do short-term investors bring additional risk to the market and cause prices to deviate from fundamental values? Based on an extensive dataset of property transactions and a policy shock that substantially raised the cost of short-term trading in Hong Kong, we estimate ‘real estate risk’ with and without short-term trading based on return predictability, return volatility, and price dispersion. Our results show that as short-term investors exit the market, market returns are less predictable and less volatile, while prices are less dispersed cross-sectionally. Consistent with herding models in behavioral finance, the findings suggest that short-term investors are momentum traders who do not enhance price efficiency.     

Do price limits hurt the market?

Under an artificial stock market composed of bounded-rational and heterogeneous traders, this paper examines whether or not price limits generate the negative effects on the market. Through testing the volatility spillover hypothesis, the delayed price discovery hypothesis, and the trading interference hypothesis, we find that no evidence of volatility spillover is observed. However, the phenomena of delayed price discovery and trading interference indeed exist, and their significance depends on the level of the price limits.     

Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes

Given that underlying assets in financial markets exhibit stylized facts such as leptokurtosis, asymmetry, clustering properties and heteroskedasticity effect, this paper applies the stochastic volatility models driven by tempered stable Lévy processes to construct time changed tempered stable Lévy processes (TSSV) for financial risk measurement and portfolio reversion. The TSSV model framework permits infinite activity jump behaviors of returns dynamics and time varying volatility consistently observed in financial markets by introducing time changing volatility into tempered stable processes which specially refer to normal tempered stable (NTS) distribution as well as classical tempered stable (CTS) distribution, capturing leptokurtosis, fat tailedness and asymmetry features of returns in addition to volatility clustering effect in stochastic volatility. Through employing the analytical characteristic function and fast Fourier transform (FFT) technique, the closed form formulas for probability density function (PDF) of returns, value at risk (VaR) and conditional value at risk (CVaR) can be derived. Finally, in order to forecast extreme events and volatile market, we perform empirical researches on Hangseng index to measure risks and construct portfolio based on risk adjusted reward risk stock selection criteria employing TSSV models, with the stochastic volatility normal tempered stable (NTSSV) model producing superior performances relative to others.     

Adverse effects of leverage and short-selling constraints in a financial market model with heterogeneous agents

This paper investigates the impact of leverage and short-selling constraints on financial market stability. Investors׳ demand is modelled in a well-known asset pricing model with heterogeneous beliefs. In particular, I generalise the heterogeneous agents model of Brock and Hommes (1998) and Anufriev and Tuinstra (2013) to allow for leverage constraints as well as a short-selling tax. I consider two examples of adaptive belief systems describing the coevolution of prices and investors׳ beliefs. First, if the market is inhabited by fundamentalist and chartist traders, demand constraints have potential adverse effects and may restrict the stabilising fundamentalist strategy such that mispricing and price volatility increase. Second, if the market is inhabited by fundamentalists, optimists and pessimists with fixed beliefs, demand constraints drive down price volatility, but mispricing remains. The results suggest the stabilising effects of demand constraints in financial markets are limited. Only if asset prices are too high compared to fundamentals, policy makers should consider constraining leverage ratios in order to deflate financial bubbles.     

GARCH模型族在沪深300中的比较研究

风险测量一直是金融研究领域的热门话题,而如何构建合适的模型来衡量风险自然而然成为众多学者研究的关注点.VaR方法是当今应用最广泛的衡量金融风险的方法之一,其核心又在构建良好的波动率估计模型.GARCH模型族能很好地描述股指波动率呈现的重尾、波动性聚集、杠杆效用等,是当前效果比较好的条件异方差性的模型.本文着重研究基于GARCH模型族(GARCH、EGARCH、PGARCH)在不同分布假定下(高斯分布、t分布、广义误差分布)的表现,从而计算出沪深300的在险价值( VaR),比较分析模型拟合效果,选出适合的模型,对规范国内沪深300的风险管理提供了理论依据.     

A comparison of different trading protocols in an agent-based market

We compare price dynamics of different market protocols (batch auction, continuous double auction and dealership) in an agent-based artificial exchange. In order to distinguish the effects of market architectures alone, we use a controlled environment where allocative and informational issues are neglected and agents do not optimize or learn. Hence, we rule out the possibility that the behavior of traders drives the price dynamics. Aiming to compare price stability and execution quality in broad sense, we analyze standard deviation, excess kurtosis, tail exponent of returns, volume, perceived gain by traders and bid-ask spread. Overall, a dealership market appears to be the best candidate, generating low volume and volatility, virtually no excess kurtosis and high perceived gain.     

Cross-sectional quantile regression for estimating conditional VaR of returns during periods of high volatility

Evaluating value at risk (VaR) for a firm’s returns during periods of financial turmoil is a challenging task because of the high volatility in the market. We propose estimating conditional VaR and expected shortfall (ES) for a given firm’s returns using quantile regression with cross-sectional (CSQR) data about other firms operating in the same market. An evaluation using US market data between 2000 and 2020 shows that our approach has certain advantages over a CAViaR model. Identification of low-risk firms and a reduction in computing times are additional advantages of the new method described.